M-How to calculate force on a surface due to a beam of particles?

[debwaldy]

Homework Statement

hi,so iv been trying to work out this problem but I am stuck because i don't understand what the lux in the question is,could anyone explain it to me?



the question says:

a beam of helium atoms is incident at an angle of 60 degrees on a flat surface of area 0.2 m^2. each atom has a velocity of 3* 10^7 m s^-1 and the beam flux is 10^16 atoms m^-2 s^-1.assuming the beam covers the whole surface what is the force on the surface?

Homework Equations

im guessing beam flux is perhaps the intensity,or the amount of atoms which wud pass through 1m^2 of surface in one second?and how exactly could i relate this to the question?should i multiply it by 0.2m^2 to figure out how many wud pass through the surface area in the question in one second?
any hints or direction would be greatly appreciated

The Attempt at a Solution

 

[Andrew Mason]

the question says:

a beam of helium atoms is incident at an angle of 60 degrees on a flat surface of area 0.2 m^2. each atom has a velocity of 3* 10^7 m s^-1 and the beam flux is 10^16 atoms m^-2 s^-1.assuming the beam covers the whole surface what is the force on the surface?

Homework Equations

im guessing beam flux is perhaps the intensity,or the amount of atoms which wud pass through 1m^2 of surface in one second?and how exactly could i relate this to the question?should i multiply it by 0.2m^2 to figure out how many wud pass through the surface area in the question in one second?
any hints or direction would be greatly appreciated

No guessing about it. That is what it is.

Assume that the He atoms collide elastically with the surface. What is the momentum imparted to the surface by one collision? (what is the change in momentum of the He atom in the collision?) What is the rate of change of momentum (ie change of momentum per unit time)? How is that related to the "force"?

AM

 

[steve12]

thanks..so do i need to know the mass of a helium atom to answer this question?

so far iv said: the change in momentutm = (3.0*10^7)(mass of he atom)(sin60)(2)=5.1961*10^7(mass of he atom)

according to my book the rate of change of momentum= (z component of momentum)( z component of velocity)/(height)

the height of what though?how do i relate this to the area i am given?
and do i need to get the z component of the beam flux for my calculations,or do i just multiply the beam flux by 0.2m^2 to get the amount of atoms that pass through 0.2m^2 in 1 sec?

 

[Andrew Mason]

thanks..so do i need to know the mass of a helium atom to answer this question?

so far iv said: the change in momentutm = (3.0*10^7)(mass of he atom)(sin60)(2)=5.1961*10^7(mass of he atom)

according to my book the rate of change of momentum= (z component of momentum)( z component of velocity)/(height)
the height of what though?how do i relate this to the area i am given?

I am not sure what the height refers to but would appear to have nothing to do with this problem.

and do i need to get the z component of the beam flux for my calculations,or do i just multiply the beam flux by 0.2m^2 to get the amount of atoms that pass through 0.2m^2 in 1 sec?

Yes. Just work out the change of momentum per second. How many of these collisions occur per second on this area?

Or more formally:

\Delta p = 2mv\sin\theta

Since the speed and angle do not change:

\frac{dp}{dt} = 2vsin\theta \frac{dm}{dt}

What is dm/dt (the mass flow per unit time) striking this surface?

AM